Solve the following quadratic equation by factorization:
$\frac{1}{x\ -\ 1}\ –\ \frac{1}{x\ +\ 5}\ =\ \frac{6}{7},\ x\ ≠\ 1,\ -5$
Given:
Given quadratic equation is $\frac{1}{x\ -\ 1}\ –\ \frac{1}{x\ +\ 5}\ =\ \frac{6}{7},\ x\ ≠\ 1,\ -5$.
To do:
We have to solve the given quadratic equation by factorization.
Solution:
$\frac{1}{x\ -\ 1}\ –\ \frac{1}{x\ +\ 5}\ =\ \frac{6}{7}$
$\frac{1(x+5)-1(x-1)}{(x-1)(x+5)}=\frac{6}{7}$
$7(x+5-x+1)=6(x-1)(x+5)$ (On cross multiplication)
$42=6(x^2+5x-x-5)$
$x^2+4x-5=\frac{42}{6}$
$x^2+4x-5-7=0$
$x^2+4x-12=0$
$x^2+6x-2x-12=0$
$x(x+6)-2(x+6)=0$
$(x+6)(x-2)=0$
$x+6=0$ or $x-2=0$
$x=-6$ or $x=2$
The roots of the given quadratic equation are $-6$ and $2$. 
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